Preclinical Pharmacokinetics
Service |
||
|
http://server.ccl.net/cgi-bin/ccl/message.cgi?1997+11+22+001 |
CCL November 22, 1997 [001] | |||||||
Saturday 1997 Nov 22 >From E. Lewars To: CCL Subj: Extended Hueckel --another summary I post another summary connected with my question (see below) because I have received another helpful letter, and because I have myself summed up the situation (below). ORIGINAL Q: Hello, What do people out there in netland think of the *current* status of the extended Hueckel method that was popularized by Roald Hoffmann, starting ca. 1963? It was, I think, the first generally applicable method, in the sense that it was not limited to planar pi electron arrays and could in principle perform geometry optimizations. Is it the general view that it is essentially obsolete, having been displaced by more sophisticated methods like MNDO and its decendants AM1 and PM3? Does it have some advantages over AM1 and PM3? Thanks E. Lewars ================ Letter from Dr Carlo Mealli: Almost as a hobby and also thanks to the help of some enthusiastic collaborators (first of all Dr. D.M.Proserpio), I have long worked to develop a handy graphic interface (package CACAO) to the numerical results of ehmo calculations (the basic programs of Roald Hoffmann at Cornell). I am very much aware of the shortcomings of the method in terms of highly reliable quantitative results. Mainly, the problems arise from neglecting the inter-electronic terms. Under these circumstances it is impossible to trust blindly a quantitative response associated, for example, with geometry optimization or with the energetics of an electronic transition. Still most of the times "the trends" are correct and there is a lot to learn from trends! If used "cum grano salis" (i.e. always referring to the e common concepts of chemical bonding, stereochemistry and reactivity), the method provides a lot of quick, useful and reliable information. The rigourous subdivision of the MOs in terms of symmetry properties (remem- ber the relevance of the Conservation of Orbital Symmetry ideas expressed by Roald Hoffmann) is dense of chemical meanings. Thus, if a low symmetry molecule is analyzed starting from the conformer with the highest possible symmetry, the evolution of the MOs and the redistribution of the electrons in them do almost invariably point toward the correct solution. Moreover it is clearly seen where the electronic problems arise from in the conformers with higher symmetry. In other words, the Perturbation Theory works well and the ehmo method helps to interpret it beautifully. Nowadays with the ubiquitous PCs, it is fast and easy to perform these calculations at will and to explore many different deformational trends and/or reaction pathways. The graphics more than the pure numbers are the e helpful interpretational tool and also the non-specialists (the experi- mental chemists, the teachers, the students, etc.) can now seek a suited MO description of the chemical bonding in a molecule or series of molecules. But there is a good point to continue to exploit the ehmo method= also for those who perform high level theoretical studies. My viewpoint is that ehmo cannot be substitutive but is a coadjutant of the latter methods most of which (from AM1 on) provide no interpretational tools, no eventual insight to the user. As in an explorative approach, a preliminary ehmo analysis= sheds light in the field where the higher level computations are meant = to be performed. Moreover, I notice myself from comparisons that the basic qua= ntitative results are very often consistent. For example, the frontier MOs = from the ehmo and those from accurate ab-initio methods correspond in energy order, symmetry and composition. When this is the case, one can strategically use the ehmo method to interpret to basic underpinnings of the given quantitative result. Beside the list of geometrical parameters of an optimized geometry, the chemist needs to know the electronic factors which affect the latter in order to understand the role, say, of some me substituents. The ultimate goal of theory is to favour the planning of new experiments. Much chemistry has been interpreted in the past 20-30 years thanks to the ehmo method because it is a powerful telescope to see Perturbation theory at work. In my opinion ehmo cannot be dismissed as obsolete especial= ly now that personal computers allow to construct a MO description of ch= emical bonding almost as easily as the Valence Bond description is constructed using paper and pencil. Dr. Carlo Mealli ============================================================================ Dr. Carlo Mealli ISSECC - CNR, Via Nardi 39, 50132 Firenze, Italy Tel 0039-55-2346653, Fax 2478366 e-mail: mealli at.at cacao.issecc.fi.cnr.it ============================================================================= Finally, _my_ ideas now; thanks to all who helped in forming them. ---- Strengths and weaknesses of the EHM STRENGTHS One big advantage of the EHM over more elaborate semiempirical methods and ab initio and DFT is that the EHM can be applied to large systems containing almost any element. The EHM can treat esentially all elements, since the only element-specific parameter needed is the (valence-state) ionization potential [1], which is generally available. In contrast, more elaborate semiempirical methods have not been parameterized for many elements (altho' recent parameteri- zations of PM3 and MNDO for transition metals make these much more generally useful than hitherto). For ab initio and DFT methods, basis sets may not be available for elements of interest, and besides ab initio and even DFT are hundreds of times slower than the EHM and are limited to much smaller systems. The applicability of the EHM to large systems and to a variety of elements is one reason why it has been extensively applied to polymeric and solid-state structures [2]. the EHM is faster than more elaborate semiempirical methods, partly because the Fock matrix yields to be diagonalized only once to yield the eigenvalues and eigenvectors (the eigenvectors must be transformed back to those of the original nonorthogonalized matrix). In contrast, methods like AM1 and PM3 (as well as ab initio calculations) require repeated matrix diagonalization because the Fock matrix must be iteratively refined in the SCF procedure. The spartan reliance of the EHM on a paucity of empirical parameters makes it relatively easy (in the right hands) to interpret its results, which depend, in the last analysis, only on geometry (which affects overlap integrals) and ionization potentials. With a strong dose of chemical intuition this has enabled the method to yield powerful insights [3]. The applicability to large systems, including polymers and solids, containing almost any kind of atom, and the relative transparency of the physical basis of the results, are the main advantages of the EHM. Surprisingly for such a conceptually simple approach, the EHM has a theoretically-based advantage over otherwise more elaborate semiempirical methods, in that it treats orbital overlap properly: AM1 and PM3, for example, use the _neglect of differential overlap_ (NDO) approximation, meaning that they take S_ij = delta_ij, as in the simple Hueckel method. The EHM can thus give superior results [4]. The EHM is a very valuable teaching tool because it follows straightforwardly from the simple Hueckel method yet uses overlap integrals and matrix orhtogonalization in the same fashion as the mathematically more elaborate ab initio procedure. Finally, the EHM, albeit more elaborately parameterized than in its original incarnation, has recently been shown to be a serious competitor to the very useful and popular semiempirical AM1 method for calculating molecular geometries [5]. WEAKNESSES The weaknesses of the standard EHM probably arise at least in part from the fact that it does not (contrast the ab initio method) take into account electron spin or electron-electron repulsion, ignores the fact that molecular geometry is partly determined by internuclear repulsions, and makes no attempt to overcome these defects by parameterization. The standard EHM gives, by and large, poor geometries and energies. Although it predicts a CH bond length of ca. 1.0 A, it yields CC bond lengths of 1.92, 1.47 and 0.85 for ethane, ethene and ethyne, respectively, cf the actual values of 1.53, 1.33 and 1.21 A, and although the favored conformation of an alkane is usually correctly identified, the energy barriers and differences are only in modest agreement with experiment [6]. Because of this inability to reliably calculate geometries, EHM calculations are usually not used for geometry optimizations, but rather utilize experimental bond lengths and angles. [1] J. Hinze, H H. Jaffe, J Am Chem Soc 84 (1962) 540; A Stockis, R. Hoffmann 102 (1980) 2952 [2] R. Hoffmann, "Solids and Surfaces: A Chemist's View of Bonding in Extended Structures", VCH publishers, 1988. [3] (a) The Woodward-Hoffman rules: R. B. Woodward, R. Hoffmann, "The Conservation of Orbital Symmetry", Academic Press, 1970. (b) Counterintuitive orbital mixing: J. H. Ammeter, H.-B. Buergi, J. C. Thibeault, R Hoffmann, J Am Chem Soc 100 (1978) 3686. [4] Rationalizing nonplanar CC double bonds: J. Spanget-Larsen, R Gleiter, Tetrahedron, 39 (1983) 3345. [5] S. L. Dixon, P C Jurs, J Comp Chem 15 (1994) 733. [6] R. Hoffmann, J Chem Phys 39 (1963) 1397. ===================== Similar Messages 03/22/1998: RESPONSE TO EHM REF REQUEST 08/01/1996: Re: CCL:M:Heat of formation calculation using MOPAC. 03/02/1992: Oh, boy, oh, boy! Real scientific controversy! 04/28/1994: Semi-empirical methods revisited 11/02/1995: summary AM1 vs PM3 04/12/1994: AM1 vs. PM3 05/08/1995: AM1 vs. PM3 08/01/1995: Spin contamination, effect on energy and structure. 04/23/1992: Huckel MO Theory software 08/03/1995: ACS Chicago - CINF Abstracts - 29 pages document - Raw Message Text |